1. Stated problem: Find the remainder when the polynomial $$2x^3 + 3x^2 - 2x + 2$$ is divided by $$x+3$$. 2. According to the Remainder Theorem, the remainder of a polynomial $$f(x)$$ divided by $$x - a$$ is $$f(a)$$. 3. Here, the divisor is $$x+3$$, which can be rewritten as $$x - (-3)$$, so $$a = -3$$. 4. Substitute $$x = -3$$ into the polynomial: $$f(-3) = 2(-3)^3 + 3(-3)^2 - 2(-3) + 2$$ 5. Calculate step-by-step: $$2(-27) + 3(9) + 6 + 2 = -54 + 27 + 6 + 2$$ 6. Simplify further: $$(-54 + 27) + (6 + 2) = -27 + 8 = -19$$ 7. Therefore, the remainder when $$2x^3 + 3x^2 - 2x + 2$$ is divided by $$x+3$$ is $$\boxed{-19}$$.